Victory stops a run of seven straight defeats for the Welshmen and moves the basement boys to within four points of safety.
Roberts struck on 71 minutes to chalk up a real shock win over the league leaders.
Boss Brain Little praised his midfielders match winning chip.
"It was an excllent goal, he had players round him and it was a great chip.
"We knew we had to stop them scoring and defend well but to get a win was fantastic."
The 29-year-old hit a vital goal for the sinking Dragons giving a glimmer of hope for League Two survival.
The former Wigan Athletic man helped his side to their first win since early December.
Boss Little will be hoping for an uptrun in fortunes on the back of this result.